"But is selling publically accessible art into private hands so only the privileged few can see it the right way?"
Who said private hands?
The commercial art world is a profit-making business and more often than not, the national galleries are outbid on some of the most important art in the world - the Chester Beatty in Dublin puts on regular displays of art
Why can't the Vatican offer its art at a realistic price to the nation - or even have it held in trust and shared with other nations - we were lucky enough to see two exhibitions o Van Gogh's works and the Tutankhamun riches in London.
The Catholic Church can hardly plead poverty with its investments and financial support ?

Due to revelations, power of the Catholic Church has waned in the last couple of decades and that decline continues steadily and internationally
Some way to go yet but if that decline continues it is going to end up as a much reduced church with a chokable number of assets
There is nothing to stop it from selling those assets (almost certainly to te highest bidder) to make up its losses
Jim Carroll